Finite Group Databasebeta

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C2×#72236967 #72344183

order6144
automorphism?
homologyAbelianization (H1) = C24×C4 · Schur multiplier (H2) = C211

Aliases

direct productC2×#72236967

Splittings

FittingC2×#6372744 ⋊ D3

Subgroups

subgroupG/H
centerC2×C4C22×#1020⋊C2
commutator, hypocenter#997C24×C4
FrattiniC22×C4C24×S4
FittingC2×#6372744D3
socleC22C2×C4×#1020⋊C2
prime radicalC22×#11714162C2
cosocle#5950C25
hypercenterC2×M16#1020⋊C2
LCSG ▷ #997
UCSC1 ◁ C2×C4 ◁ C2×M16

At least 14918 conjugacy classes of subgroups; only the 947 normal subgroups are shown.

Full subgroup data →

Conjugacy classes & character table

248 conjugacy classes — view the full character table.

GAP

Past the SmallGroups library coverage — no SmallGroups id.